Cacio e Plantain

Pour neutral oil to a depth of 1/4 inch into a large skillet, and heat over medium. Fry plantain slices in hot oil in a single layer until deep golden brown, about 3 minutes per side. Transfer to a plate lined with paper towels; let cool 5 minutes.

Process plantains in a food processor until a coarse paste forms, about 30 seconds. With processor running, gradually drizzle in olive oil and heavy cream, stopping to scrape sides of bowl as needed. With processor running, add egg yolks, vinegar, 1/2 cup water, and 1 teaspoon salt. Process until combined and smooth, about 30 seconds. Pour mixture through a fine wire-mesh strainer, pressing with the back of a spoon to yield about 3 1/2 cups; discard solids.

Bring remaining 4 quarts water to a boil in a large stockpot over medium-high. Stir in remaining 1/4 cup salt. Add spaghetti, and cook, stirring occasionally, until al dente, 9 to 11 minutes. Meanwhile, gently heat sauce in a 12-inch skillet over low, stirring often to prevent the sauce from separating or overcooking the eggs.

Drain pasta, reserving 1/2 cup pasta cooking liquid. Add pasta to sauce in skillet, and increase heat to medium. Cook, tossing constantly, until pasta is evenly coated, about 2 minutes, adding reserved pasta cooking liquid, 2 tablespoons at a time, if needed to thin sauce. Season with salt to taste. Sprinkle with Parmesan cheese, pepper, and cilantro. Serve immediately.